Finding the Area of a Sector using Trigonometric Functions

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SUMMARY

The discussion focuses on calculating the area of a sector using trigonometric functions, specifically sine and cosine. The area was computed using the formula A = 1/2 × r² × θ, where r is the radius (approximately 16.8319 cm) and θ is the angle in radians (0.5707). A minor correction was noted in the area calculation, with the correct value being 80.83 cm² instead of 80.84 cm². Participants explored alternative approaches to the sine function, including the use of cosine.

PREREQUISITES
  • Understanding of trigonometric functions (sine and cosine)
  • Familiarity with the formula for the area of a sector
  • Basic calculator skills for trigonometric calculations
  • Knowledge of radians and their application in geometry
NEXT STEPS
  • Study the derivation of the area of a sector formula
  • Learn about the relationship between sine and cosine in trigonometric identities
  • Explore advanced applications of trigonometric functions in geometry
  • Investigate the use of radians versus degrees in mathematical calculations
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Students, educators, and professionals in mathematics or engineering who are looking to deepen their understanding of trigonometric applications in geometry.

chwala
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Homework Statement
See attached
Relevant Equations
Area of sector
My interest is on part (c) only.

1648079111365.png


Wow, this was a nice one! boggled me a little bit anyways; my last steps to solution,
##A= \dfrac{1}{2} ×16.8319^2 × 0.5707=80.84cm^2## bingo!
Any other approach apart from using sine?
Cheers guys
 
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chwala said:
Any other approach apart from using sine?

Yes ! Using the cosine of angle FEH (which happens to be the sine of 1 radian, but that may well be a coincidence :smile: )

Your calculator needs new batteries: not 80.84 but 80.83 :wink: !

##\ ##
 
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